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Hydrodynamics of Vegetated Channels

  • Jochen AberleEmail author
  • Juha Järvelä
Chapter
Part of the GeoPlanet: Earth and Planetary Sciences book series (GEPS)

Abstract

Hydrodynamics of vegetated channels and streams is a rapidly developing research area, and this chapter summarizes the current knowledge considering both aquatic and riparian zones. The benefit of an advanced parameterization of plant morphology and biomechanical properties is highlighted. For this purpose, the response of flexible and foliated plants and plant communities to the flow is illustrated, and advanced models for the determination of drag forces of flexible plants are described. Hydrodynamic processes governing flow patterns in vegetated flows are presented for submerged and emergent conditions considering spatial scales ranging from the leaf to the vegetated reach scale.

Keywords

Rivers and floodplains Aquatic vegetation Riparian vegetation Hydrodynamics Flow field Flow resistance Modelling Parameterization 

References

  1. Aberle J, Järvelä J (2013) Flow resistance of emergent rigid and flexible floodplain vegetation. J Hydraul Res 51(1):33–45Google Scholar
  2. Ackerman JD, Okubo A (1993) Reduced mixing in a marine macrophyte canopy. Funct Ecol 7:305–309Google Scholar
  3. Albayrak I, Nikora V, Miler O, O’Hare M (2011) Flow–plant interactions at a leaf scale: effects of leaf shape, serration, roughness and flexural rigidity. Aquat Sci 74(2):267–286Google Scholar
  4. Albayrak I, Nikora V, Miler O, O’Hare M (2014) Flow–plant interactions at leaf, stem and shoot scales: drag, turbulence, and biomechanics. Aquat Sci 76(2):269–294Google Scholar
  5. Alben S, Shelley M, Zhang J (2002) Drag reduction through self-similar bending of a flexible body. Nature 420(6915):479–481Google Scholar
  6. Antonarakis AS, Richards KS, Brasington J, Muller E (2010) Determining leaf area index and leafy tree roughness using terrestrial laser scanning. Water Resour Res 46(W06510). doi: 10.1029/2009WR008318
  7. Cameron SM, Nikora VI, Albayrak I, Miler O, Stewart M, Siniscalchi F (2013) Interactions between aquatic plants and turbulent flow: a field study using stereoscopic PIV. J Fluid Mech 732:345–372Google Scholar
  8. Chakrabarti S (2002) The theory and practice of hydrodynamics and vibration. World Scientific, SingaporeGoogle Scholar
  9. Chen L, Stone MC, Acharya K, Steinhaus KA (2011) Mechanical analysis for emergent vegetation in flowing fluids. J Hydraul Res 49(6):766–774Google Scholar
  10. Chen Z, Jiang C, Nepf H (2013) Flow adjustment at the leading edge of a submerged aquatic canopy. Water Resour Res 49(9):5537–5551Google Scholar
  11. Coles D (1956) The law of the wake in the turbulent boundary layer. J Fluid Mech 1(2):191–226Google Scholar
  12. Curran JC, Hession WC (2013) Vegetative impacts on hydraulics and sediment processes across the fluvial system. J Hydrol 505:364–376Google Scholar
  13. Czarnomski N, Tullos D, Thomas R, Simon A (2012) Effects of vegetation canopy density and bank angle on near-bank patterns of turbulence and Reynolds stresses. J Hydraul Eng 138(11):974–978Google Scholar
  14. de Langre E (2008) Effects of wind on plants. Annu Rev Fluid Mech 40:141–168Google Scholar
  15. de Langre E, Gutierrez A, Cossé J (2012) On the scaling of drag reduction by reconfiguration in plants. Comptes Rendus Mécanique 340(1–2):35–40Google Scholar
  16. de Lima A, Izumi N (2014) Linear stability analysis of open-channel shear flow generated by vegetation. J Hydraul Eng 140(3):231–240Google Scholar
  17. Dijkstra JT, Uittenbogaard RE (2010) Modeling the interaction between flow and highly flexible aquatic vegetation. Water Resour Res 46(W12547), 125. doi: 10.11029/12010WR009246
  18. Dittrich A, Aberle J (2010) Die Vegetation an Fliessgewässern aus dem Blickwinkel eines Hydraulikers. Ingenieurbiologie/Genie Biologique 3:37–42Google Scholar
  19. Dittrich A, Koll K, Becker K. (2002) Resistance of local flood berm vegetation in compound channels. In: Proceedings of the 5th International Conference Hydro-Science and EngineeringGoogle Scholar
  20. Dittrich A, Aberle J, Schoneboom T (2012) Drag forces and flow resistance of flexible riparian vegetation. In: Rodi W, Uhlmann M (eds) Environmental fluid mechanics: memorial colloquium on environmental fluid mechanics in honour of Professor Gerhard H Jirka. CRC Press, London, pp 195–215Google Scholar
  21. Folkard AM (2011) Vegetated flows in their environmental context: a review. Eng Comput Mech 164(EM1):3–24Google Scholar
  22. Ghisalberti M, Nepf HM (2002) Mixing layers and coherent structures in vegetated aquatic flows. J Geophys Res 107(C2):3.1–3.11Google Scholar
  23. Ghisalberti M, Nepf HM (2004) The limited growth of vegetated shear layers. Water Resour Res 40, doi: 10.1029/2003WR002776
  24. Godin C, Caraglio Y (1998) A multiscale model of plant topological structures. J Theor Biol 191(1):1–46Google Scholar
  25. Gosselin F, de Langre E (2011) Drag reduction by reconfiguration of a poroelastic system. J Fluid Struct 27(7):1111–1123Google Scholar
  26. Gosselin F, de Langre E, Machado-Almeida B (2010) Drag reduction of flexible plates by reconfiguration. J Fluid Mech 650:319–341Google Scholar
  27. Green JC (2005a) Modelling flow resistance in vegetated streams: review and development of new theory. Hydrolog Process 19:1245–1259Google Scholar
  28. Green JC (2005b) Comparison of blockage factors in modelling the resistance of channels containing submerged macrophytes. River Res Appl 21:671–686Google Scholar
  29. Grant PF, Nickling WG (1998) Direct field measurement of wind drag on vegetation for application to windbreak design and modelling. Land Degrad Dev 9:57–66Google Scholar
  30. Gurnell A (2014) Plants as river system engineers. Earth Surf Proc Land 39(1):4–25Google Scholar
  31. Gurnell A, Petts G (2006) Trees as riparian engineers: the Tagliamento River, Italy. Earth Surf Proc Land 31(12):1558–1574Google Scholar
  32. Gurnell AM, van Oosterhout MP, de Vlieger B, Goodson JM (2006) Reach-scale interactions between aquatic plants and physical habitat: River Frome, Dorset. River Res Appl 22:667–680Google Scholar
  33. Hoerner S (1965) Fluid-dynamic drag. Brick TownGoogle Scholar
  34. Jalonen J, Järvelä J (2014) Estimation of drag forces caused by natural woody vegetation of different scales. J Hydrodyn 26(4):608–623. doi: 10.1016/S1001-6058(14)60068-8 Google Scholar
  35. Jalonen J, Järvelä J, Aberle J (2012) Vegetated flows: drag force and velocity profiles for foliated plant stands. In: Murillo R (ed) Proceedings of river flow 2012, international conference on fluvial hydraulics, September 2012, San José 2012. Taylor & Francis, LondonGoogle Scholar
  36. Jalonen J, Järvelä J, Aberle J (2013) Leaf area index as vegetation density measure for hydraulic analyses. J Hydraul Eng 139(5):461–469Google Scholar
  37. Jalonen J, Järvelä J, Koivusalo H, Hyyppä H (2014) Deriving floodplain topography and vegetation characteristics for hydraulic engineering applications by means of terrestrial laser scanning. J Hydraul Eng 140(11):04014056. doi: 10.1061/(ASCE)HY.1943-7900.0000928 Google Scholar
  38. Jalonen J, Järvelä J, Virtanen J-P, Vaaja M, Kurkela M, Hyyppä H (2015) Determining characteristic vegetation areas by terrestrial laser scanning for floodplain flow modeling. Water 7(2):420–437. doi: 10.3390/w7020420 Google Scholar
  39. James CS, Goldbeck UK, Patini A, Jordanova AA (2008) Influence of foliage on flow resistance of emergent vegetation. J Hydraul Res 46(4):536–542Google Scholar
  40. Janauer GA, Schmidt-Mumm U, Reckendorfer W (2013) Ecohydraulics and aquatic macrophytes: assessing the relationship in river floodplains. In: Maddock I, Harby A, Kemp P, Wood P (eds) Ecohydraulics—an integrated approach. Wiley, Chichester, pp 245–260Google Scholar
  41. Järvelä J (2002) Flow resistance of flexible and stiff vegetation: a flume study with natural plants. J Hydrol 269:44–54Google Scholar
  42. Järvelä J (2004) Determination of flow resistance caused by non-submerged woody vegetation. Int J River Basin Manage 2(1):61–70Google Scholar
  43. Järvelä J (2005) Effect of submerged flexible vegetation on flow structure and resistance. J Hydrol 307(1–4):233–241Google Scholar
  44. King AT, Tinoco RO, Cowen EA (2012) A k–ε turbulence model based on the scales of vertical shear and stem wakes valid for emergent and submerged vegetated flows. J Fluid Mech 701:1–39Google Scholar
  45. Klaasen GJ, van Urk A (1985) Resistance to flow of floodplains with grasses and hedges. In: proceedings of 21st IAHR Congress, Melbourne, AustraliaGoogle Scholar
  46. Knight DW (2013) River hydraulics—a view from midstream. J Hydraul Res 51(1):2–18Google Scholar
  47. Kouwen N, Unny TE (1973) Flexible roughness in open channels. J Hydr Div 99(5):713–728Google Scholar
  48. Kouwen N (1992) Modern approach to design of grassed channels. J Irrig Drain Eng 118(5):733–743Google Scholar
  49. Kouwen N, Fathi-Moghadam M (2000) Friction factors for coniferous trees along rivers. J Hydraul Eng 126(10):732–740Google Scholar
  50. Kubrak E, Kubrak J, Rowinski PM (2008) Vertical velocity distributions through and above submerged, flexible vegetation. Hydrological Sci J 53(4):905–920Google Scholar
  51. Kubrak E, Kubrak J, Rowiński P (2012) Influence of a method of evaluation of the curvature of flexible vegetation elements on vertical distributions of flow velocities. Acta Geophys 60(4):1098–1119Google Scholar
  52. Li RM, Shen W (1973) Effect of tall vegetations on flow and sediment. J Hydraul Div 99(HY5):793–814Google Scholar
  53. Lightbody AF, Nepf HM (2006) Prediction of near-field shear dispersion in an emergent canopy with heterogeneous morphology. Environ Fluid Mech 6:477–488Google Scholar
  54. Lindner K (1982) Der Strömungswiderstand von Pflanzenbeständen. Mitt. Leichtweiß-Institut für Wasserbau No. 75, Braunschweig, Technische Universität Braunschweig, Germany, in GermanGoogle Scholar
  55. Luhar M, Nepf HM (2011) Flow-induced reconfiguration of buoyant and flexible aquatic vegetation. Limnol Oceanogr 56(6):2003–2017Google Scholar
  56. Luhar M, Nepf HM (2013) From the blade scale to the reach scale: a characterization of aquatic vegetative drag. Adv Water Resour 51:305–316Google Scholar
  57. Mertens W (2006) Hydraulisch-sedimentologische Berechnungen naturnah gestalteter Fliessgewässer. Deutsche Vereinigung für Wasserwirtschaft, Abwasser und Abfall e.V., Hennef, in GermanGoogle Scholar
  58. Miler O, Albayrak I, Nikora V, O’Hare M (2011) Biomechanical properties of aquatic plants and their effects on plant–flow interactions in streams and rivers. DOI, Aquat Sci. doi: 10.1007/s00027-00011-00188-00025 Google Scholar
  59. Miler O, Albayrak I, Nikora V, O’Hare M (2014) Biomechanical properties and morphological characteristics of lake and river plants: implications for adaptations to flow conditions. Aquat Sci. doi: 10.1007/s00027-014-0347-6 Google Scholar
  60. Neary V, Constantinescu S, Bennett S, Diplas P (2012) Effects of vegetation on turbulence, sediment transport, and stream morphology. J Hydraul Eng 138(9):765–776Google Scholar
  61. Nepf HM (1999) Drag, turbulence, and diffusion in flow through emergent vegetation. Water Resour Res 35(2):479–489Google Scholar
  62. Nepf HM (2012a) Hydrodynamics of vegetated channels. J Hydraul Res 50(3):262–279Google Scholar
  63. Nepf HM (2012b) Flow and transport in regions with aquatic vegetation. Annu Rev Fluid Mech 44:123–142Google Scholar
  64. Nepf HM, Vivoni ER (2000) Flow structure in depth-limited, vegetated flow. J Geophys Res 105(C12):28457–28557Google Scholar
  65. Nepf H, Ghisalberti M (2008). Flow and transport in channels with submerged vegetation. Acta Geophys 56(3). doi: 10.2478/s11600-11008-10017-y
  66. Nikora N, Nikora V, O’Donoghue T (2013a) Velocity profiles in vegetated open-channel flows: Combined effects of multiple mechanisms. J Hydraul Eng 139(10):1021–1032Google Scholar
  67. Nikora V (2010a) Hydrodynamics of aquatic ecosystems: an interface between ecology, biomechanics and environmental fluid mechanics. River Res Appl 26(4):367–384Google Scholar
  68. Nikora V (2010b) Hydrodynamics of aquatic ecosystems: current state, challenges, and prospects. In: Proceedings of 17th Australasian fluid mechanics conference, Auckland New ZealandGoogle Scholar
  69. Nikora VI, Rowinski PM (2008) Rough-bed flows in geophysical, environmental, and engineering systems: double-averaging approach and its applications. Acta Geophys 56(3):529–533Google Scholar
  70. Nikora V, Koll K, McEwan I, McLean S, Dittrich A (2004) Velocity distribution in the roughness layer of rough-bed flows. J Hydraul Eng 130(10):1036–1042Google Scholar
  71. Nikora V, McEwan I, McLean S, Coleman S, Pokrajac D, Walters R (2007a) Double-averaging concept for rough-bed open-channel and overland flows: theoretical background. J Hydraul Eng 133(8):873–883Google Scholar
  72. Nikora V, McLean S, Coleman S, Pokrajac D, McEwan I, Campbell L, Aberle J, Clunie D, Ka Koll (2007b) Double-Averaging concept for rough-bed open-channel and overland flows: applications. J Hydraul Eng 133(8):884–895Google Scholar
  73. Nikora V, Ballio F, Coleman S, Pokrajac D (2013b) Spatially averaged flows over mobile rough beds: Definitions, averaging theorems, and conservation Equations. J Hydraul Eng 139(8):803–811Google Scholar
  74. Okamoto T, Nezu I (2009) Turbulence structure and “Monami” phenomena in flexible vegetated open-channel flows. J Hydraul Res 47(6):798–810Google Scholar
  75. Okamoto TA, Nezu I (2013) Spatial evolution of coherent motions in finite-length vegetation patch flow. Env Fluid Mech 13:417–434Google Scholar
  76. Osterkamp WR, Hupp CR, Stoffel M (2012) The interactions between vegetation and erosion: new directions for research at the interface of ecology and geomorphology. Earth Surf Proc Land 37:23–36Google Scholar
  77. Palmer VJ (1945) A method for designing vegetated waterways. Agric Eng 26(12):16–520Google Scholar
  78. Pasche E, Rouvé G (1985) Overbank flow with vegetatively roughened flood plains. J Hydraul Eng 111(9):1262–1278Google Scholar
  79. Paul M, Henry PYT, Thomas RE (2014) Geometrical and mechanical properties of four species of northern European brown macroalgae. Coast Eng 84:73–80Google Scholar
  80. Petryk S, Bosmajian G (1975) Analysis of flow through vegetation. J Hydraul Div 101(7):871–884Google Scholar
  81. Plew D (2011) Depth-averaged drag coefficient for modeling flow through suspended canopies. J Hydraul Eng 137(2):234–247Google Scholar
  82. Poggi D, Porporato A, Ridolfi L, Albertson JD, Katul GG (2004) The effect of vegetation density on canopy sub-layer turbulence. Bound-Layer Meteor 111:565–587Google Scholar
  83. Puijalon S, Léna J-P, Riviére N, Champagne JY, Rostan JC, Bornette G (2008) Phenotypic plasticity in response to mechanical stress: hydrodynamic performance and fitness of 4 aquatic plant species. New Phytol 177:907–917Google Scholar
  84. Rhee DS, Woo H, Kwon BA, Ahn HK (2008) Hydraulic resistance of some selected vegetation in open channel flows. River Res Appl 24:673–687Google Scholar
  85. Ricardo AM, Koll K, Franca MJ, Schleiss AJ, Ferreira RML (2014) The terms of turbulent kinetic energy budget within random arrays of emergent cylinders. Water Resour Res 50(5):4131–4148Google Scholar
  86. Richardson DM, Holmes PM, Esler KJ, Galatowitsch SM, Stromberg JC, Kirkman SP, Pyšek P, Hobbs RJ (2007) Riparian vegetation: degradation, alien plant invasions, and restoration prospects. Divers Distrib 13(1):126–139Google Scholar
  87. Sand-Jensen K (2003) Drag and reconfiguration of freshwater macrophytes. Freshwat Biol 48(2):271–283Google Scholar
  88. Sanjou M, Nezu I (2011) Turbulence structure and concentration exchange property in compound open-channel flows with emergent trees on the floodplain edge. Int J River Basin Manag 9(3–4):181–193Google Scholar
  89. Schlichting H, Gersten K (2006) Grenzschicht-Theorie. Springer, BerlinGoogle Scholar
  90. Schoneboom T, Aberle J, Dittrich A (2011) Spatial variability, mean drag forces, and drag coefficients in an array of rigid cylinders. Exp Methods Hydrau Res Geoplanet: Earth Planet Sci 1:255–265. doi: 10.1007/978-3-642-17475-9_18 Google Scholar
  91. SCS (1954) Handbook of channel design for soil and water conservation. Soil conservation service SCS-TP-61. U.S. Department of Agriculture, Washington, D.CGoogle Scholar
  92. Shiono K, Knight DW (1991) Turbulent open-channel flows with variable depth across the channel. J Fluid Mech 222:617–646Google Scholar
  93. Shucksmith JD, Bocall JB, Guymer I (2010) Effects of emergent and submerged natural vegetation on longitudinal mixing in open channel flow. Water Resour Res 46, W04504. doi:04510.01029/02008WR007657Google Scholar
  94. Siniscalchi F, Nikora VI (2012) Flow-plant interactions in open-channel flows: a comparative analysis of five freshwater plant species. Water Resour Res 48(W05503). doi: 10.1029/2011WR011557
  95. Siniscalchi F, Nikora V (2013) Dynamic reconfiguration of aquatic plants and its interrelations with upstream turbulence and drag forces. J Hydraul Res 51(1):46–55Google Scholar
  96. Siniscalchi F, Nikora VI, Aberle J (2012) Plant patch hydrodynamics in streams: mean flow, turbulence, and drag forces. Water Resour Res 48(W01513). doi: 10.1029/2011WR011050
  97. Sinoquet H, Rivet P (1997) Measurement and visualization of the architecture of an adult tree based on a three-dimensional digitising device. Trees 11(5):265–270Google Scholar
  98. Souliotis D, Prinos P (2011) Effect of a vegetation patch on turbulent channel flow. J Hydraul Res 49(2):157–167Google Scholar
  99. Statzner B, Lamoroux N, Nikora V, Sagnes P (2006) The debate about drag and reconfiguration of freshwater macrophytes: comparing results obtained by three recently discussed approaches. Freshwat Biol 51(11):2173–2183Google Scholar
  100. Stephan U, Gutknecht D (2002) Hydraulic resistance of submerged flexible vegetation. J Hydrol 269:27–43Google Scholar
  101. Stoesser T, Palau Salvador G, Rodi W, Diplas P (2009) Large eddy simulation of turbulent flow through submerged vegetation. Transport Porous Med 78:347–365Google Scholar
  102. Stoesser T, Kim SJ, Diplas P (2010) Turbulent flow through idealized emergent vegetation. J Hydraul Eng 136(12):1003–1017Google Scholar
  103. Stone MC, Chen L, McKay SK, Goreham J, Acharya K, Fischenich C, Stone AB (2013) Bending of submerged woody riparian vegetation as a function of hydraulic flow conditions. River Res Appl 29:195–205Google Scholar
  104. Sukhodolov A, Sukhodolova T (2010) Case study: effect of submerged aquatic plants on turbulence structure in a lowland river. J Hydraul Eng 136(7):434–446Google Scholar
  105. Sukhodolov AN, Sukhodolova TA (2012) Vegetated mixing layer around a finite-size patch of submerged plants: part 2. turbulence statistics and structures. Water Resour Res 48(12):W12506. doi: 10.1029/2011WR011805 Google Scholar
  106. Sukhodolova TA, Sukhodolov AN (2012) Vegetated mixing layer around a finite-size patch of submerged plants: 1. theory and field experiments. Water Resour Res 48(10):W10533. doi: 10.1029/2011WR011804 Google Scholar
  107. Sun X, Shiono K (2009) Flow resistance of one-line emergent vegetation along the floodplain edge of a compound open channel. Adv Water Resour 32:430–438Google Scholar
  108. Tanino Y, Nepf H (2008) Lateral dispersion in random cylinder arrays at high Reynolds number. J Fluid Mech 600:339–371Google Scholar
  109. Temple DM (1999) Flow resistance of grass-lined channel banks. Appl Eng Agric 15(2):129–133Google Scholar
  110. Thomas RE, Johnson MF, Frostick LE, Parsons DR, Bouma TJ, Dijkstra JT, Eiff O, Gobert S, Henry PY, Kemp P, McLelland SJ, Moulin FY, Myrhaug D, Neyts A, Paul M, Penning WE, Puijalon S, Rice SP, Stanica A, Tagliapietra D, Tal M, Tørum A, Vousdoukas MI (2014) Physical modelling of water, fauna and flora: knowledge gaps, avenues for future research and infrastructural needs. J Hydraul Res. doi: 10.1080/00221686.2013.876453 Google Scholar
  111. Vandenbruwaene W, Temmerman S, Bouma TJ, Klaassen PC, De Vries MB, Callaghan DP, van Steeg P, Dekker F, van Duren LA, Martini E, Balke T, Biermans G, Schoelynck J, Meire P (2011) Flow interaction with dynamic vegetation patches: implications for biogeomorphic evolution of a tidal landscape. J Geophys Res 116, F01008, doi:01010.01029/02010JF001788Google Scholar
  112. Vargas-Luna A, Crosato A, Uijttewaal WSJ (2015) Effects of vegetation on flow and sediment transport: comparative analyses and validation of predicting models. Earth Surf Process Land 40:157–176. doi: 10.1002/esp.3633 Google Scholar
  113. Västilä K, Järvelä J (2014) Modeling the flow resistance of woody vegetation using physically based properties of the foliage and stem. Water Resour Res 50(1):229–245Google Scholar
  114. Västilä K, Järvelä J, Aberle J (2013) Characteristic reference areas for estimating flow resistance of natural foliated vegetation. J Hydrol 492:49–60Google Scholar
  115. Vogel S (1994) Life in moving fluids: the physical biology of flow, 2nd edn. Princeton University Press, PrincetonGoogle Scholar
  116. Vogel S (2009) Leaves in the lowest and highest winds: temperature, force and shape. New Phytol 183(1):13–26Google Scholar
  117. Whittaker P, Wilson C, Aberle J, Rauch HP, Xavier P (2013) A drag force model to incorporate the reconfiguration of full-scale riparian trees under hydrodynamic loading. J Hydraul Res 51(5):569–580Google Scholar
  118. Wilkerson GV (2007) Flow through trapezoidal and rectangular channels with rigid cylinders. J Hydraul Eng 133(5):521–533Google Scholar
  119. Wilson CAME, Horrit MS (2002) Measuring the flow resistance of submerged grass. Hydrolog Process 16:2589–2598Google Scholar
  120. Wilson CAME, Hoyt J, Schnauder I (2008) Impact of foliage on the drag force of vegetation in aquatic flows. J Hydraul Eng 134(7):885–891Google Scholar
  121. Yager EM, Schmeeckle MW (2013) The influence of vegetation on turbulence and bed load transport. J Geophys Res Earth Surf 118(3):1585–1601Google Scholar
  122. Yen BC (2002) Open channel flow resistance. J Hydraul Eng 128(1):20–39Google Scholar
  123. Zeng C, Li CW (2014) Measurements and modeling of open-channel flows with finite semi-rigid vegetation patches. Env Fluid Mech 14(1):113–134Google Scholar
  124. Zong L, Nepf H (2010) Flow and deposition in and around a finite patch of vegetation. Geomorphology 116:363–372Google Scholar
  125. Zong L, Nepf H (2011) Spatial distribution of deposition within a patch of vegetation. Water Resour Res 47(W03516). doi:03510.01029/02010WR009516Google Scholar

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© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Norwegian University of Science and TechnologyTrondheimNorway
  2. 2.Aalto University School of EngineeringEspooFinland

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